def get_static_surrogate(D):
N = 200
X = np.random.randn(N, D)
est = KernelExpLiteGaussian(sigma=1, lmbda=.1, D=D, N=N)
est.fit(X)
return est
def get_static_surrogate(D):
N = 200
X = np.random.randn(N, D)
est = KernelExpLiteGaussian(sigma=1, lmbda=.1, D=D, N=N)
est.fit(X)
return est
class KernelExpLiteGaussianSurrogate(StaticSurrogate):
def __init__(self, ndim, sigma, lmbda, N):
self.surrogate = KernelExpLiteGaussian(sigma=sigma,
lmbda=lmbda,
N=N,
D=ndim)
def train(self, samples):
self.surrogate.fit(samples)
def log_pdf_gradient(self, x):
return self.surrogate.grad(x)
def test_third_order_derivative_tensor_execute():
if not theano_available:
raise SkipTest("Theano not available.")
sigma = 1.
lmbda = 1.
N = 100
D = 2
X = np.random.randn(N, D)
est = KernelExpLiteGaussian(sigma, lmbda, D, N)
est.fit(X)
est.third_order_derivative_tensor(X[0])
def test_hessian_execute():
if not theano_available:
raise SkipTest("Theano not available.")
sigma = 1.
lmbda = 1.
N = 100
D = 2
X = np.random.randn(N, D)
est = KernelExpLiteGaussian(sigma, lmbda, D, N)
est.fit(X)
est.hessian(X[0])
def test_third_order_derivative_tensor_execute():
if not theano_available:
raise SkipTest("Theano not available.")
sigma = 1.
lmbda = 1.
N = 100
D = 2
X = np.random.randn(N, D)
est = KernelExpLiteGaussian(sigma, lmbda, D, N)
est.fit(X)
est.third_order_derivative_tensor(X[0])
def test_hessian_execute():
if not theano_available:
raise SkipTest("Theano not available.")
sigma = 1.
lmbda = 1.
N = 100
D = 2
X = np.random.randn(N, D)
est = KernelExpLiteGaussian(sigma, lmbda, D, N)
est.fit(X)
est.hessian(X[0])
def get_kmc_static_kernel():
num_steps_min, num_steps_max, step_size_min, step_size_max = get_hmc_parameters()
target, momentum = get_target_momentum()
N = 200
X = np.random.randn(N, momentum.D)
est = KernelExpLiteGaussian(sigma=1, lmbda=.1, D=momentum.D, N=N)
est.fit(X)
surrogate = get_static_surrogate(momentum.D)
kmc = KMCStatic(surrogate, target, momentum, num_steps_min, num_steps_max, step_size_min, step_size_max)
return kmc
def get_kmc_static_kernel():
num_steps_min, num_steps_max, step_size_min, step_size_max = get_hmc_parameters(
)
target, momentum = get_target_momentum()
N = 200
X = np.random.randn(N, momentum.D)
est = KernelExpLiteGaussian(sigma=1, lmbda=.1, D=momentum.D, N=N)
est.fit(X)
surrogate = get_static_surrogate(momentum.D)
kmc = KMCStatic(surrogate, target, momentum, num_steps_min, num_steps_max,
step_size_min, step_size_max)
return kmc
for i, sigma in enumerate(log_sigmas):
est = KernelExpLiteGaussian(np.exp(sigma), lmbda, D, N)
# this is an array num_repetitions x num_folds, each containing a objective
xval_result = est.xvalidate_objective(X, num_folds=5, num_repetitions=2)
O[i] = np.mean(xval_result)
O_lower[i] = np.percentile(xval_result, 10)
O_upper[i] = np.percentile(xval_result, 90)
# best parameter
best_log_sigma = log_sigmas[np.argmin(O)]
# visualisation
plt.figure()
plt.plot([best_log_sigma, best_log_sigma], [np.min(O), np.max(O)], 'r')
plt.plot(log_sigmas, O, 'b-')
plt.plot(log_sigmas, O_lower, 'b--')
plt.plot(log_sigmas, O_upper, 'b--')
plt.xlim([np.min(log_sigmas) - 1, np.max(log_sigmas) + 1])
plt.xlabel("log sigma")
plt.ylabel("objective")
plt.title("lmbda=%.4f" % lmbda)
plt.legend(["Best sigma", "Performance"])
plt.legend(["Best sigma", "Performance", "80% percentile"])
plt.tight_layout()
est.sigma = np.exp(best_log_sigma)
est.fit(X)
visualise_fit_2d(est, X)
plt.show()
